A radial-ply pneumatic tire carcass has a reverse curvature, an outwardly concave shape, centered about the tire's equatorial plane. A wedge of elastomeric material is positioned above or below the belt structure of the tire. If positioned above the belt structure, the wedge is used with a carcass cord angle in the range from 65.degree. to 80.degree.. This carcass structure also may be used when the wedge is positioned between the belt structure and carcass. The tire has an aspect ratio less than 75%, but 40% to 65% is preferred. The wedge has a shape on its radially inner side that is similar to a low amplitude cosine function. Particularly when the wedge is above the belt structure (providing both it and the belt structure with a reverse curvature), the belt cord angle is less than a "critical angle" of about 25.degree.. The invention can provide a radial-ply belted tire which has "natural shape" in the portion of the radial carcass underlying the belt structure, but the "natural shape" is for those low cord angles used in the belt structure.